Lagrange reversion theorem
From Wikipedia, the free encyclopedia
- This page is about Lagrange reversion. For inversion, see Lagrange inversion theorem.
In mathematics, the Lagrange reversion theorem gives series or formal power series expansions of certain implicitly defined functions; indeed, of compositions with such functions.
Let z be a function of x and y in terms of another function f such that
- z = x + yf(z)
Then for any function g,
for small y. If z is the identity
[edit] External links
- Lagrange Inversion [Reversion] Theorem on MathWorld
- Cornish-Fisher expansion, an application of the theorem
- Article on equation of time contains an application to Kepler's equation
